The long-term goal of this research is to develop new statistical methodology for the design and analysis of cancer screening trials. Cancer screening is the major technique for early detection of cancer, hence for disease control. The effectiveness of the screening program directly depends on lead time, which is the length of time the diagnosis is advanced by screening. The property of the lead time for the screening detected cases has been derived in today's literature, mainly in a stable disease model. However, the proportion of people who does not benefit from the screening is not addressed; further more, the long-term contribution of screening has not been evaluated. The specific aims are: (1) Derive the exact probability distribution for the lead time in a periodic screening program, for both the screening-detected cases and the interval cases, in both stable and nonstable disease models. Hence we can make statistical inference about the lead time, estimate the proportion of people who truly benefit from periodic screenings in a long-term scenario, and the proportion that does not. The proposed distribution of the lead time will depend on the sensitivity, the sojourn time distribution, the transition probability into the preclinical state, and the screening time intervals. The proposed method will be verified by extensive simulations. (2) Apply the proposed method to aid in developing the optimal design of periodic screening; in particular, choosing screening time intervals for groups of people with different risks. User-friendly software will be developed and made available to the research community. In summary, the proposed research will be an aid to increase the efficiency and reduce the cost of future periodic screening trials.